Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26022089 | C2 | semidirect |
| 2. #26018328 | C2 | semidirect |
| 3. #26018225 | C2 | semidirect |
| 4. #26018168 | C2 | semidirect |
| 24. Q32×C89 | C8 | semidirect |
| 25. SD32×C89 | C8 | semidirect |
| 26. D16×C89 | C8 | semidirect |
| 76. C89 | #12047 | semidirect |
| 89. Q32 | #10623494 | semidirect |
| 90. SD32 | #10623494 | semidirect |
| 91. D16 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022089 | 2 |
| #26018328 | 2 |
| #26018225 | 2 |
| #26018168 | 2 |
| C89×#2178 | 2 |
| #12047 | 89 |